In this work, we propose a formulation to predict modulated coherent structures in shock-containing jets. First, the shock-cell structure for a given flow condition is approximated using PSE applied to a modelled ideally expanded jet. This solution is then used to define a new shock-containing mean flow, around which the Navier-Stokes equations are linearised. By means of a Floquet ansatz, a new set of equations is obtained, in which the positive and negative components of the modulation (related to the local shock-cell wavenumber) are considered in the response vector. The final equations have the same shape as in PSE and are solved in the same fashion, rendering the name parabolised Floquet equations [1]}. We show that the formulation is more restrictive than PSE due to the repetition of the modes in the eigenspectrum of the linear operators (as in [2]}), which may also require substantially larger spatial steps for the march, depending on the flow conditions and the frequency of analysis.
